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<li class="navelem"><a class="el" href="namespace_s_p_h.html">SPH</a></li><li class="navelem"><b>solid_dynamics</b></li><li class="navelem"><a class="el" href="class_s_p_h_1_1solid__dynamics_1_1_kirchhoff_stress_relaxation_first_half.html">KirchhoffStressRelaxationFirstHalf</a></li>  </ul>
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<a href="#pub-methods">Public Member Functions</a> &#124;
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<p>Decompose the stress into particle stress includes isotropic stress and the stress due to non-homogeneous material properties. The preliminary shear stress is introduced by particle pair to avoid spurious stress and deformation. Note that, for the shear stress term, due to the mismatch of the divergence contribution between the pair-wise second-order derivative Laplacian formulation and particle-wise first-order gradient formulation, a correction factor slight large than one is introduced. Note that, if you see time step size goes unusually small, it may be due to the determinate of deformation matrix become negative. In this case, you may need decrease CFL number when computing time-step size.  
 <a href="class_s_p_h_1_1solid__dynamics_1_1_kirchhoff_stress_relaxation_first_half.html#details">More...</a></p>

<p><code>#include &lt;<a class="el" href="elastic__dynamics_8h_source.html">elastic_dynamics.h</a>&gt;</code></p>

<p>Inherits <a class="el" href="class_s_p_h_1_1solid__dynamics_1_1_base_stress_relaxation_first_half.html">SPH::solid_dynamics::BaseStressRelaxationFirstHalf</a>.</p>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a4fa802adf637f5e843410bf512008b66"><td class="memItemLeft" align="right" valign="top"><a id="a4fa802adf637f5e843410bf512008b66"></a>
&#160;</td><td class="memItemRight" valign="bottom"><b>KirchhoffStressRelaxationFirstHalf</b> (<a class="el" href="class_s_p_h_1_1_base_body_relation_inner.html">BaseBodyRelationInner</a> &amp;inner_relation)</td></tr>
<tr class="separator:a4fa802adf637f5e843410bf512008b66"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="inherit_header pub_methods_class_s_p_h_1_1solid__dynamics_1_1_base_stress_relaxation_first_half"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_s_p_h_1_1solid__dynamics_1_1_base_stress_relaxation_first_half')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="class_s_p_h_1_1solid__dynamics_1_1_base_stress_relaxation_first_half.html">SPH::solid_dynamics::BaseStressRelaxationFirstHalf</a></td></tr>
<tr class="memitem:a79d498f2051ae46c0638bf6d38ca42d9 inherit pub_methods_class_s_p_h_1_1solid__dynamics_1_1_base_stress_relaxation_first_half"><td class="memItemLeft" align="right" valign="top"><a id="a79d498f2051ae46c0638bf6d38ca42d9"></a>
&#160;</td><td class="memItemRight" valign="bottom"><b>BaseStressRelaxationFirstHalf</b> (<a class="el" href="class_s_p_h_1_1_base_body_relation_inner.html">BaseBodyRelationInner</a> &amp;inner_relation)</td></tr>
<tr class="separator:a79d498f2051ae46c0638bf6d38ca42d9 inherit pub_methods_class_s_p_h_1_1solid__dynamics_1_1_base_stress_relaxation_first_half"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:af33573cffb1afa786c5ec7d8c9875708 inherit pub_methods_class_s_p_h_1_1solid__dynamics_1_1_base_elastic_relaxation"><td class="memItemLeft" align="right" valign="top"><a id="af33573cffb1afa786c5ec7d8c9875708"></a>
&#160;</td><td class="memItemRight" valign="bottom"><b>BaseElasticRelaxation</b> (<a class="el" href="class_s_p_h_1_1_base_body_relation_inner.html">BaseBodyRelationInner</a> &amp;inner_relation)</td></tr>
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<tr class="memitem:a80cb542de2046cff21b3cdcaad4a31fa inherit pub_methods_class_s_p_h_1_1_particle_dynamics1_level"><td class="memItemLeft" align="right" valign="top"><a id="a80cb542de2046cff21b3cdcaad4a31fa"></a>
&#160;</td><td class="memItemRight" valign="bottom"><b>ParticleDynamics1Level</b> (<a class="el" href="class_s_p_h_1_1_s_p_h_body.html">SPHBody</a> &amp;sph_body)</td></tr>
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virtual void&#160;</td><td class="memItemRight" valign="bottom"><b>parallel_exec</b> (Real dt=0.0) override</td></tr>
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<tr class="memitem:a5a289cd33420210bb55ec704f4c45351 inherit pub_methods_class_s_p_h_1_1_interaction_dynamics_with_update"><td class="memItemLeft" align="right" valign="top"><a id="a5a289cd33420210bb55ec704f4c45351"></a>
&#160;</td><td class="memItemRight" valign="bottom"><b>InteractionDynamicsWithUpdate</b> (<a class="el" href="class_s_p_h_1_1_s_p_h_body.html">SPHBody</a> &amp;sph_body)</td></tr>
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<tr class="memitem:a7d757e98a171eb8d845732d7d5035310 inherit pub_methods_class_s_p_h_1_1_interaction_dynamics"><td class="memItemLeft" align="right" valign="top"><a id="a7d757e98a171eb8d845732d7d5035310"></a>
&#160;</td><td class="memItemRight" valign="bottom"><b>InteractionDynamics</b> (<a class="el" href="class_s_p_h_1_1_s_p_h_body.html">SPHBody</a> &amp;sph_body)</td></tr>
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<tr class="memitem:ac0b1853fed55e6d3f080f3317f875080 inherit pub_methods_class_s_p_h_1_1_particle_dynamics"><td class="memItemLeft" align="right" valign="top"><a id="ac0b1853fed55e6d3f080f3317f875080"></a>
&#160;</td><td class="memItemRight" valign="bottom"><b>ParticleDynamics</b> (<a class="el" href="class_s_p_h_1_1_s_p_h_body.html">SPHBody</a> &amp;sph_body)</td></tr>
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<a class="el" href="class_s_p_h_1_1_s_p_h_body.html">SPHBody</a> *&#160;</td><td class="memItemRight" valign="bottom"><b>getSPHBody</b> ()</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>DataDelegateInner</b> (<a class="el" href="class_s_p_h_1_1_base_body_relation_inner.html">BaseBodyRelationInner</a> &amp;body_inner_relation)</td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pro-methods"></a>
Protected Member Functions</h2></td></tr>
<tr class="memitem:a8496540e5c3327656446d54a6efa12bb"><td class="memItemLeft" align="right" valign="top"><a id="a8496540e5c3327656446d54a6efa12bb"></a>
virtual void&#160;</td><td class="memItemRight" valign="bottom"><b>Initialization</b> (<a class="el" href="classsize__t.html">size_t</a> index_i, Real dt=0.0) override</td></tr>
<tr class="separator:a8496540e5c3327656446d54a6efa12bb"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9ade42d79d22ff00b7845b01d727954a"><td class="memItemLeft" align="right" valign="top"><a id="a9ade42d79d22ff00b7845b01d727954a"></a>
virtual void&#160;</td><td class="memItemRight" valign="bottom"><b>Interaction</b> (<a class="el" href="classsize__t.html">size_t</a> index_i, Real dt=0.0) override</td></tr>
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<tr class="inherit_header pro_methods_class_s_p_h_1_1solid__dynamics_1_1_base_stress_relaxation_first_half"><td colspan="2" onclick="javascript:toggleInherit('pro_methods_class_s_p_h_1_1solid__dynamics_1_1_base_stress_relaxation_first_half')"><img src="closed.png" alt="-"/>&#160;Protected Member Functions inherited from <a class="el" href="class_s_p_h_1_1solid__dynamics_1_1_base_stress_relaxation_first_half.html">SPH::solid_dynamics::BaseStressRelaxationFirstHalf</a></td></tr>
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virtual void&#160;</td><td class="memItemRight" valign="bottom"><b>Update</b> (<a class="el" href="classsize__t.html">size_t</a> index_i, Real dt=0.0) override</td></tr>
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<tr class="inherit_header pro_methods_class_s_p_h_1_1_particle_dynamics"><td colspan="2" onclick="javascript:toggleInherit('pro_methods_class_s_p_h_1_1_particle_dynamics')"><img src="closed.png" alt="-"/>&#160;Protected Member Functions inherited from <a class="el" href="class_s_p_h_1_1_particle_dynamics.html">SPH::ParticleDynamics&lt; void &gt;</a></td></tr>
<tr class="memitem:a6c3ffa11bc0514cd9eb1537b79b4975c inherit pro_methods_class_s_p_h_1_1_particle_dynamics"><td class="memItemLeft" align="right" valign="top"><a id="a6c3ffa11bc0514cd9eb1537b79b4975c"></a>
void&#160;</td><td class="memItemRight" valign="bottom"><b>setBodyUpdated</b> ()</td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pro-attribs"></a>
Protected Attributes</h2></td></tr>
<tr class="memitem:a9e1787d407e360e0d6d61bd3a77cc868"><td class="memItemLeft" align="right" valign="top"><a id="a9e1787d407e360e0d6d61bd3a77cc868"></a>
StdLargeVec&lt; Real &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>J_to_minus_2_over_dimension_</b></td></tr>
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StdLargeVec&lt; Matd &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>stress_on_particle_</b></td></tr>
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StdLargeVec&lt; Matd &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>inverse_F_T_</b></td></tr>
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const Real&#160;</td><td class="memItemRight" valign="bottom"><b>one_over_dimensions_</b> = 1.0 / (Real)Dimensions</td></tr>
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const Real&#160;</td><td class="memItemRight" valign="bottom"><b>correction_factor_</b> = 1.07</td></tr>
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Real&#160;</td><td class="memItemRight" valign="bottom"><b>rho0_</b></td></tr>
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Real&#160;</td><td class="memItemRight" valign="bottom"><b>inv_rho0_</b></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Decompose the stress into particle stress includes isotropic stress and the stress due to non-homogeneous material properties. The preliminary shear stress is introduced by particle pair to avoid spurious stress and deformation. Note that, for the shear stress term, due to the mismatch of the divergence contribution between the pair-wise second-order derivative Laplacian formulation and particle-wise first-order gradient formulation, a correction factor slight large than one is introduced. Note that, if you see time step size goes unusually small, it may be due to the determinate of deformation matrix become negative. In this case, you may need decrease CFL number when computing time-step size. </p>
</div><hr/>The documentation for this class was generated from the following files:<ul>
<li>SPHINXsys/src/shared/particle_dynamics/solid_dynamics/<a class="el" href="elastic__dynamics_8h_source.html">elastic_dynamics.h</a></li>
<li>SPHINXsys/src/shared/particle_dynamics/solid_dynamics/<a class="el" href="elastic__dynamics_8cpp.html">elastic_dynamics.cpp</a></li>
</ul>
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